Oh I don't think it is or even was a problem with it...Ok. It's the notion of an "inertial relationship", whatever that is, being in some way faster than light that I can't understand. But if it was in correspondence with Mach, I feel fairly certain it was resolved by the development of relativity, rather than remaining a problem within it.
It demonstrates Einsteins incredible desire to leave no stone upturned in discovering how this universe works, even if it meant threatening his own theories...
This is why I suggested that it all depends on what people mean when they talk about the issue of light speed in-variance.
I guess he was trying to figure out why the laws of physics are universally invariant, re: the first Postulate.
"The laws of physics are the same in all inertial frames of reference."
Testing the postulates must have taken up a lot of time for him.. I would speculate....
Then along comes the discovery of various anomalies that suggest that the 1st postulate may not be as valid as first thought. ie. Dark Flow, Great Attractor and even the CBR cold spot super void. To name only three...